Suppose [tex] f(x) = \frac{(x-3)^{4}}{x^{2}+2x} [/tex]. Find the derivative an determine the values for which it is equal to 0. So [tex] f'(x) = \frac{x^{2}+2x(4(x-3)^{3}) - (x-3)^{4}(2x+2)}{(x^{2}+2x)^{2}} [/tex]. But now how would I go about finding the values for which the derivative equals 0? [tex] f'(x) = \frac{x^{2}+2x(4(x-3)^{3}) (x-3)^{4}(2x+2)}{(x^{2}+2x)^{2}} = 0 [/tex]. Is it possible to factor? Thanks
For any fraction, let's call it [itex]\frac{A}{B}[/itex], which part will make the whole thing equal to 0? A or B?